关于超空间 H(X)/H(X;K)

IF 0.6 4区数学 Q3 MATHEMATICS

Topology and its Applications Pub Date : 2024-05-29 DOI:10.1016/j.topol.2024.108972

Florencio Corona-Vázquez, José A. Martínez-Cortez, Russell-Aarón Quiñones-Estrella, Javier Sánchez-Martínez

引用次数: 0

摘要

设 X 是连续体，K 是 X 的非空封闭子集，n 是正整数。在本文中，我们考虑超空间 2X 和 Cn(X)，它们分别由 X 的所有非空封闭子集和 X 的所有最多有 n 个分量的非空封闭子集组成。如果 H(X)∈{2X,Cn(X)}，H(X;K) 表示 H(X) 中所有元素与 K 相交的超空间。在本文中，我们将介绍商空间 H(X)/H(X;K) 的一些拓扑性质，并在现有文献中继续对其进行研究。在有限图类中，我们研究了如何确定 X 和 K 的条件，从而使 Cn(X) 和 Cn(X)/Cn(X;K) 同构，并在此方向上获得了一些特征。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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About the hyperspace H(X)/H(X;K)

Let X be a continuum, K a nonempty closed subset of X, and let n be a positive integer. In this paper, we consider the hyperspaces $2^{X}$ and $C_{n} (X)$ , consisting of all nonempty closed subsets of X and of all nonempty closed subsets of X having at most n components, respectively. If $H (X) \in {2^{X}, C_{n} (X)}$ , $H (X; K)$ denotes the hyperspace of all elements in $H (X)$ intersecting K. In this paper we present some topological properties of the quotient space $H (X) / H (X; K)$ , going forward in its study in the available literature. In the class of finite graphs, we study the problem of determining conditions on X and K such that $C_{n} (X)$ and $C_{n} (X) / C_{n} (X; K)$ are homeomorphic, obtaining in this direction some characterizations.

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来源期刊

Topology and its Applications 数学-数学

CiteScore

1.20

自引率

33.30%

发文量

251

审稿时长

6 months

期刊介绍： Topology and its Applications is primarily concerned with publishing original research papers of moderate length. However, a limited number of carefully selected survey or expository papers are also included. The mathematical focus of the journal is that suggested by the title: Research in Topology. It is felt that it is inadvisable to attempt a definitive description of topology as understood for this journal. Certainly the subject includes the algebraic, general, geometric, and set-theoretic facets of topology as well as areas of interactions between topology and other mathematical disciplines, e.g. topological algebra, topological dynamics, functional analysis, category theory. Since the roles of various aspects of topology continue to change, the non-specific delineation of topics serves to reflect the current state of research in topology. At regular intervals, the journal publishes a section entitled Open Problems in Topology, edited by J. van Mill and G.M. Reed. This is a status report on the 1100 problems listed in the book of the same name published by North-Holland in 1990, edited by van Mill and Reed.